This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.

We study categoricity in power for reduced models of first order logic without equality.

In this article, we formalize some basic facts of Z-module. In the first section, we discuss the rank of submodule of Z-module and its properties. Especially, we formally prove that the rank of any Z-module is equal to or more than that of its submodules, and vice versa, there exists a submodule with any given rank that satisfies the above condition. In the next section, we mention basic facts ...

The aim of this paper is to give a new proof for the decidability and nite model property of rst-order logic with two variables (without function symbols), using a combinatorial theorem due to Herwig. The results are proved in the framework of polyadic equality set algebras of dimension two (Pse 2). The new proof also shows the known results that the universal theory of Pse 2 is decidable and t...

We introduce a proper display calculus for (non-distributive) Lattice Logic which is sound, complete, conservative, and enjoys cut-elimination and subformula property. Properness (i.e. closure under uniform substitution of all parametric parts in rules) is the main interest and added value of the present proposal, and allows for the smoothest Belnap-style proof of cut-elimination. Our proposal ...

The result of forgetting some predicates in a first-order sentence may not exist in the sense that it might not be captured by any first-order sentences. This, indeed, severely restricts the usage of forgetting in applications. To address this issue, we propose a notion called k-forgetting, also called bounded forgetting in general, for any fixed number k. We present several equivalent characte...

We introduce generalized quantifiers, as defined in Tarskian semantics by Mostowski and Lindström, in logics using the Hodges semantics, e.g., IF-logic and dependence logic. For this we introduce the multivalued dependence atom and observe the similarities with the, by Väänänen and Grädel, newly introduced independence atom.

In this paper, we introduce EVE, a generic framework for event detection where events can also include outliers, model changes and drifts. Various methods for event detection have been proposed for different types of events. However, many of them make the same or very similar prior assumptions but use different notations and formalizations. EVE provides a general framework for event detection, ...

Let Ln be the first-order language for Nn. Thus, Ln contains the symbols =, 1, 2, . . . , n interpreted in Nn as the identity and the natural numbers 1, 2, . . . , n. By Fn we denote the set of all formulas of Ln. Hence, Fn is the smallest set such that: a. ti = tj ∈ Fn, b. if A,B ∈ Fn, then: ¬A, A → B, A∧B, A∨B, A ≡ B, ∨